Algorithmic advances are responsible for some of the most remarkable applications of computation today—from search engines and machine learning to error-correcting codes and cryptography. Yet, even now, some of the most basic algorithmic questions remain unanswered, and among these are open problems with far-reaching implications for computer security and beyond.

In this talk, Umans will describe how computer scientists identify and abstract these key problems—and how some of these puzzles encapsulate deep questions about the nature of computation itself. Additionally, he will describe a promising new approach he has helped develop that may finally yield an optimal algorithm for multiplying matrices—potentially resolving a prominent unanswered algorithmic question.